Question

0.6 - What is the least number which when divided by the numbers 3,
5, 6, 8, 10 and 12 leaves in each case a remainder 2 but which when
divided by 13 leaves no remainder?

NO SPAMMING!!!​

Answer 1

Least no. divided by 3 , 5, 6, 8, 10, 12 giving no remainder is LCM of these no.s

LCM of 3, 5, 6, 8, 10, 12 is 120 .

we have to get 2 as the remainder

So we add 2 to the LCM , but contradict is that it must be divided by 13

So the no. would be 120k + 2

to find value of k :

120k+2/13

117k + 3k + 2 / 13

117k/13 + 3k +2/13

Here 117k/13 gives remainder 0

in 3k+2 on putting the value of k =8 by hit and trial method we get remainder as 0

hence

the no. would be 120k+2

120×8+2=962